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Improving Mathematical Thinking

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Agenda

  • Problem Solving Thinking
  • Problem Solving Strategies
  • Practice

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1.

Problem Solving Thinking

I’m thinking... thinking... thinking...

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Problem Solving Thinking

  • You have a new problem
    • You’ve never seen this before! Now what?
  • Try some stuff
    • Oh, this looks hard!
  • The panic starts settling in, especially if someone is watching you and saying this is easy 😤
    • Two main approaches to anxiety:
      • Let it wash over you (rock in a stream) or
      • Fight it (you don’t have time for this!)
    • The goal is to help you relax so you can start thinking
    • Also helped by breathing and focus on your focus

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Problem Solving Thinking

  • Other ways to help with problem solving
    • Use Polya’s thinking technique
    • Get in a quiet place
    • Remove distractions (phone, computer)
  • Improve your basic skills to remove thinking time on skills
    • Your thinking energy can be devoted to the problem solving and not the technique
  • Keep confident
    • All of these problems are solvable!

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2.

Problem Solving Strategies

Different methods

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Problem Solving Strategies

  • You are ready to solve your problem
  • Now what?
  • Consider different strategies
    • Draw a diagram
    • Guess-and-check
    • Make a table
    • Try a simpler case
    • Try a more general case (this is rare, but sometimes works really well!)
    • Look for a pattern with small cases
    • Make some assumptions about your solution to get clues
    • Work backwards from a solution to the problem

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3.

Practice

Pretty much the only way to get better

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Practice

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CREDITS

Special thanks to all the people who made and released these awesome resources for free:

  • Presentation template by SlidesCarnival

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